There isn't a lot to say about the topic "fusion", but I will tell you all I know. Since I don't know a lot about it, I cannot tell you any history about it. But here goes!
The Fusion technique was a way of bringing to people together...literally. In the DBZ series, our favorite characters used it on many occasions to fight off evil. When to people are fused, so is their power, combining all into one extremely powerful warrior. When the person speaks, it sounds like both people a re speaking the same thing, but in unison. So you may be thinking, if this techinque is so powerful, why don't they ALL fuse into one "super being"? And why don't they just do this for every fight? Well, there are many reasons why this cannot be done. I have listed them below:
Requirements
1. If the two fighters mess up the Fusion Dance in any way, and they go through with it, then instead of turning into the correct form, they will transform into a very weak form.
2. A maximum of 2 warriors can be fused, once fused, they cannot combine with another. This power only lasts for a maximum of 30 minutes. Once the 30 minutes are up, the two warriors must have a resting time of about an hour or so before performing it again.
3. They learned of this technique very late into the series, so they couldn't have used it for any other battles besides the ones in the Majin Buu saga.
4. The two warriors' build, size, and especially power must be equal (but the power part was no problem for the Z warriors since they could control their power levels).
Let's DANCE!
The Fusion Dance looks pretty easy to do, but have you ever tried it? It is harder than it looks, it would take a few tries to get it right. I have shown a few pictures of the steps to perfecting the Fusion Dance:
The Alternative
Actually, the Z warriors didn't have to learn the Fusion dance, at all (although at the times of battle, it was a essencial for victory)! Instead, they could have used the Fusion Earings, known as "Potara". When they met Kaioshin and her partner, they noticed they were wearing one earing on opposite sides of the ear, meaning one wore it on the left ear, and one on the right. The earings were known as "Potara" but these special earings could not be found just anywhere, since there are was only 3 such pairs of earings known to exist. These earings were a bit different from the fusion dance. They both had their differences. One of the two must be worn on each of the warriors, on opposing ears from their partner. This technique was meant to be permanent, and so it can be only performed once in each fighter's lifetime. Instead of transforming into the same person as in the Fusion Dance, they transform into a similar being, except they will have a different name, they will look a little bit different, but will be similar in power.
Who's who??
There were actually only a couple of Fusion characters created in the Dragon Ball Z series. One of them were Goten and Trunks who formed Gotenks via Fusion Dance. The Other two were of Goku and Vegita, who formed Gogeta, via Fusion Dance, and Vejitto via Fusion Earings. Other than those three characters there were no other possibilities.